Question

The angles in a straight line are X degree, 3x degree and 6x degree. find the measure of each angle.​

Answer 1

Answer :-

• The angles of straight line are 18°, 54° and 108°.

Step-by-step explanation:

Given that,

• The angles in a straight line are (x)°, (3x)° and (6x)°

We know,

Straight line are supplementary [180°]

Therefore,

• (x)° + (3x)° + (6x)° = 180°

⇒ x + 3x + 6x = 180

⇒ 4x + 6x = 180

⇒ 10x = 180

⇒ x = 180/10

⇒ x = 18

The value of x is 18.

∴ The angles of the straight line :-

• (x)° = 18°
• (3x)° = (3*18)° = 54°
• (6x)° = (6*18)° = 108°

Hence, The angles of straight line are 18°, 54° and 108°.

Now, Verification

• x + 3x + 6x = 180

By putting the value of angles on L.H.S :-

⇒ x + 3x + 6x

⇒ 18 + 54 + 108

⇒ 72 + 108

⇒ 180

Therefore, L.H.S = R.H.S

Hence, Verified!

Answer 2

$\large {\frak {\underline { \dag \; \; Given :}}}$

• Angles on straight line are x°,3x° and 6x°

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$\large {\frak {\underline { \dag \; \; To ~ find :}}}$

• Measure of each angle.

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎

$\large {\frak {\underline { \dag \; \; Solution :}}}$

• As, we know that sum of the angles on straight line is 180°

So,

$\implies \sf { (x)° + (3x)° + (6x)° = 180°}$

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$\implies \sf { 10x = 180}$

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$\implies \sf { x = \dfrac {180}{10}}$

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$\implies \sf { x = 18°}$

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Therefore,

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎$\to \sf { First ~ angle = x° = 18°}$

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎$\to \sf { Second ~ angle = 3x° = 54°}$

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎$\to \sf { Third ~ angle = 6x° = 108°}$